The idea, step by step
Read the dependency, not the story order
A precedence table lists the activities, their durations and the activities that must finish immediately before each one can start. It describes a rule for starting work, not a compulsory order for every task. Two activities with no predecessors may start together if enough people and equipment are available.
An immediate predecessor is the last required activity on a chain. If painting follows sanding and sanding follows assembly, record sanding as painting's immediate predecessor. Assembly is still an indirect requirement, but repeating it in the table hides the useful structure. Durations must use a common unit.
Turn words into a checkable model
First name each activity with a unique label. Then ask, for each activity, 'What must already be finished?' Record all independent requirements. If equipment testing needs both wiring and assembly, write both predecessors; it is not enough to choose whichever one you expect to finish later.
Check that every predecessor label exists and that the rules do not lead back to the same activity. A cycle such as A after B and B after A prevents either task from starting. Finally, distinguish a logical dependency from a resource restriction: having only one technician is additional information that an ordinary precedence table does not automatically represent.
| Activity | Duration | Immediate predecessors |
|---|---|---|
| A | 4 | None |
| B | 3 | None |
| C | 5 | A |
| D | 4 | A |
| E | 2 | B and D |
| F | 3 | C and E |
A common trap
Writing the activity immediately above in the table as the predecessor, even when the description allows parallel work.
Instead: Table order is only a way to display the data. Use the stated dependency for each activity independently.
See the thinking
Build a small table from a description
A display needs a base A (2 days), artwork B (3 days) and final assembly C (1 day). A and B can begin immediately; C needs both. Write a precedence table.
- Give A and B no predecessors because neither needs earlier work.
- C has two independent requirements, so list A and B together.
- Keep the durations in days and list each activity once.
Remove an unnecessary predecessor
A is followed by B, B by C, and D can start only after C. A draft table lists A, B and C as the immediate predecessors of D. Correct it.
- The chain is A then B then C then D.
- Finishing C already guarantees that A and B have finished.
- Only C is an immediate predecessor of D.
Check your understanding
A requires no earlier work. B follows A. C follows B. Is A an immediate predecessor of C?
Show answer
No. B is the immediate predecessor; A is an indirect predecessor.
The direct rule for C is that B must finish. B's own rule already ensures A has finished.
Your turn
6 questions · 14 marks · Work at your own pace.
Read the questions online
- Using the display-project table, identify every activity that can start at time 0.2 marks
A school display project. Times are in days. Activity Duration Immediate predecessors A 4 None B 3 None C 5 A D 4 A E 2 B and D F 3 C and E - Using the display-project table, state the immediate predecessors and all indirect predecessors of F.3 marks
A school display project. Times are in days. Activity Duration Immediate predecessors A 4 None B 3 None C 5 A D 4 A E 2 B and D F 3 C and E - A delivery A takes 1 day. Cutting B and cleaning C each follow A. Fitting D needs both B and C. Write just the predecessor column for A, B, C and D.3 marks
- A table says A follows C, B follows A, and C follows B. Explain why this is not a workable project plan.2 marks
- Painting P follows priming R, which follows cleaning C. Should the immediate predecessors of P be C and R? Explain.2 marks
- Two independent jobs have no predecessors, but both need the same single crane. Does the precedence table alone guarantee that they can occur together?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Using the display-project table, identify every activity that can start at time 0.2 marks
A school display project. Times are in days. Activity Duration Immediate predecessors A 4 None B 3 None C 5 A D 4 A E 2 B and D F 3 C and E A and B have 'None' in the predecessor column.
All other activities require at least one earlier activity.
A and B. - Using the display-project table, state the immediate predecessors and all indirect predecessors of F.3 marks
A school display project. Times are in days. Activity Duration Immediate predecessors A 4 None B 3 None C 5 A D 4 A E 2 B and D F 3 C and E F needs C and E.
C needs A; E needs B and D; D needs A.
A, B and D are earlier requirements but not immediate predecessors of F.
Immediate: C and E. Indirect: A, B and D. - A delivery A takes 1 day. Cutting B and cleaning C each follow A. Fitting D needs both B and C. Write just the predecessor column for A, B, C and D.3 marks
B and C each depend directly on delivery.
D needs both branches to finish.
A: none; B: A; C: A; D: B and C. - A table says A follows C, B follows A, and C follows B. Explain why this is not a workable project plan.2 marks
A waits for C, C waits for B, and B waits for A.
There is no starting activity to break the cycle.
It contains the cycle A → B → C → A, so no activity can begin. - Painting P follows priming R, which follows cleaning C. Should the immediate predecessors of P be C and R? Explain.2 marks
Cleaning is already required before priming.
Completing R therefore guarantees completion of C.
No; list R only. - Two independent jobs have no predecessors, but both need the same single crane. Does the precedence table alone guarantee that they can occur together?2 marks
Logical independence allows parallel scheduling in the basic model.
A shared crane is a resource constraint that must be modelled or scheduled separately.
No.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 General Mathematics: discrete models, project scheduling and assignment. Activity-on-arrow conventions are used for project networks; technology may verify calculations but does not replace interpreting the model.
Official curriculum source ↗